In order to obtain a detailed verification of the theory of thermal conduction in dielectric crystals, measurements have been made on a number of artificial sapphire crystals between 2° and 100° K. In the region of the maximum there are variations in conductivity between crystals from different sources. The highest conductivities measured are about 140 W/cm deg., which suggests that estimates of several hundred watts for the maxima of ideal sapphire crystals are not unreasonable. At sufficiently low temperatures the conductivity of a very perfect, long crystal with rough surfaces is observed, in agreement with Casimir’s theory of boundary scattering, to be proportional to T 3 and to the radius; the phonon mean free path is then nearly equal to the crystal diameter. Imperfect crystals show some anomalous effects. The extension of Casimir’s theory to apply to short specimens has been verified. Perfect crystals with smooth surfaces exhibit some specular reflexion of phonons; a statistical description of the surface is proposed which leads to the observed variation of this effect with temperature and is compatible with the results of interferometric examination of the surface.

Measurements of the thermal conductivity of TiO 2 , KCl, LiF and of three types of diamond below room temperature are reported. Although the first three crystals were very pure there are great deviations from the form of conductivity curve predicted by Peierls for perfect crystals. A consideration of these and other results suggests that the conductivity of many crystals which have been measured is limited by the existence of more than one isotopic species of the chemical elements involved. These give rise to irregularities in the arrangement of atomic mass in the crystals and are a source of phonon scattering. A theory of this effect is given and is compared with the experimental results for the nine substances for which there are sufficient data. The agreement is satisfactory; only for diamond does it appear necessary to invoke impurities as well as isotopes to explain the observed conductivity.

The thermal conductivity between 2° and 100°K has been measured on synthetic sapphire single crystals and on sintered alumina, before and after reactor and γ-ray irradiations. Reactor irradiation appears to introduce two types of thermal resistivity-producing defects, one of which is dominant at low temperatures. The only effect of γ irradiation is an extra thermal resistivity at low temperatures which saturates for quite small doses. This saturation value seems to depend on the initial perfection of the crystal and is increased by reactor produced damage. At present, detailed information about the defects cannot be derived from thermal conductivity measurements alone.